1. Field of the Invention
The present invention relates to the rolling of metal strips and, more particularly, to techniques for maintaining the strips flat during the rolling process.
2. Prior Art
Sheet metal is produced by rolling slabs, bars, or other relatively massive workpieces into thin, elongated strips. Although finish rolling often occurs near room temperature (cold rolling), the initial workpiece reduction from its slab form is done at elevated temperature in a facility known as a hot strip mill. The product of the hot strip mill may be further processed and further reduced in thickness, or it may be sold directly for applications requiring thicker strip materials. Where hot-rolled strip is an intermediate product subject to further rolling, its width and thickness dimensions may be somewhat less critical than where it is the final product. In either case, however, its flatness, or freedom from waviness, is important since excess waviness interferes with both subsequent processing and eventual fabrication of the strip into a finished product.
Waviness in rolled strip results from unequal elongation across the strip width due to unequal percentage thickness reduction across the strip width. A region of strip which is elongated more than other strip regions will exhibit waviness.
In order to reduce the thickness of the strip, the strip is passed between successive stands having two opposed rolls which are designed to support large rolling forces. In a "two high" stand only two rolls are present, while in a "four high" stand upper and lower work rolls contact the strip and are themselves contacted by upper and lower backup rolls of much larger diameter. Even the relatively rigid "four high" assembly experiences deflection under the bending effort of rolling forces which range from 500 to 3000 tons in strip rolling applications. To compensate for deflection, the work rolls may be ground, or contoured, so that their diameter at mid-length is greater than their diameter at the ends. This diameter difference is referred to as roll "crown".
Roll crown is not constant during a rolling operation, but varies as the roll temperature increases or decreases through contact with (a) the hot workpiece and (b) cooling water used in the process. Roll crown changes due to nonuniform temperature variations across the roll may exceed 0.01 inch. During the rolling process, the roll crown is further altered by surface wear in the regions of contact with the workpiece. Work rolls are changed relatively frequently to maintain good surface conditions but may exhibit wear in excess of 0.01 inch. In addition to work roll dimension changes, backup rolls wear due to friction from their contact with the work rolls. Although backup roll wear rates are much lower than work roll wear rates, the time between backup roll changes is sufficiently greater than the accumulated wear may be of the same order as work roll wear.
These roll crown-influencing factors combine at each mill stand to produce some strip thickness variation across strip width. The difference between strip thickness near its edge and at its center is referred to as "strip crown". With the exception of roll wear, all of the factors which influence roll crown and roll deflection can be used to control strip crown. Roll temperature can be controlled by the use of roll coolant. Deflection can be controlled by proper choice of thickness reduction which determines the associated roll separating force. Roll grinding practices normally are chosen to be compatible with the planned rolling practice. Finally, supplementary roll bending systems can be provided to alter the effective roll crown by applying bending moments to the work rolls or backup rolls with hydraulic cylinders.
Whatever the method of controlling roll crown and strip crown, the strip crowns in successive rolling stands must result in essentially equal elongation of all elements of the strip across its width or waviness eventually will result. Equal element elongation will be achieved if all strip elements receive identical percentage thickness reductions in each rolling stand. Expressed another way, the percent strip crown must be maintained essentially constant during the successive reductions in thickness.
These concepts are well understood in the context of both cold rolling and hot rolling. In hot rolling, most recent techniques have attempted to meet the constant percentage thickness reduction requirement by proper choice of thickness reduction and associated rolling force. These methods attempt to model mathematically the thermal roll crown changes in the work rolls, the wear pattern in the work rolls and backup rolls, and the deflection of the work rolls under nonuniform roll separating forces. These methods then attempt to choose a thickness reduction such that the combination of roll crown factors and roll deflection factors produces a delivery strip crown which bears the proper relationship to the entry strip crown at each rolling stand. In some variations of this strategy, the calculations are limited to the last three or four rolling stands.
While this prior art strategy produces somewhat better results than strategies which take no account of entry and delivery strip crown relationships, it is obvious that in the absence of flatness feedback, the results often will be unreliable. That is, the prior techniques are "predictive" because they calculate in advance the expected results of a rolling schedule and do not rely on measured values to determine if in fact the proper strip crown relationships are being produced. The difficulties inherent in a predictive approach can be appreciated by recognizing that a workpiece 0.1 inch thick produced with a strip crown 0.001 inch greater than a crown produced under conditions of uniform elongation will experience approximately 0.1 percent less elongation at the center than at the edges. The extra edge elongation will produce an edge waviness of about 0.8 inch amplitude, in the absence of tension. Since uncertainties in the actual loaded roll surface configuration will often exceed 0.001 inch, it is clear that waviness easily can occur with even the most sophisticated predictive technique.
Prior art strip crown control techniques in hot strip mills have analyzed the waviness problem without taking tension between roll stands into account or by assuming that interstand tension is negligible. It is well known in cold rolling to provide substantial tension between successive roll stands. This is done primarily to reduce the roll force required to effect the desired thickness reduction. It also is recognized that interstand tension acts as an aid to flatness control. The use of relatively high interstand tension has been possible in cold rolling because the elastic limits of a typical workpiece at or near room temperature are very high. Interstand tensile stresses may therefore be maintained correspondingly high without exceeding the elastic limits of the strip and, therefore, without causing undesirable interstand plastic deformation.
It is further known in cold rolling applications that nonuniform tension distributions which would have resulted from nonuniform elongation across strip width are attenuated by an amount which depends upon the length of the arc of contact, the thickness of the workpiece and the elastic moduli of the workpiece and rolls. Davies ("Preduction and Control of Strip Flatness in Cold Rolling"--W. E. Davies, et al, Metals Technology, October 1975) gives the following expression for attenuation, A, of roll crown errors in the presence of tension: ##EQU1## wherein: l=arc of contact
h=outgoing thickness PA1 E.sub.s =elastic modulus of strip PA1 E.sub.R =elastic modulus of roll.
In this respect, interstand tension influences are similar for hot and cold rolling applications. The fact that interstand tension exhibits this flatness correcting effect in hot rolling applications has probably been neglected because (1) it has been generally assumed that interstand tension levels are negligible in hot rolling, and (2) it has been incorrectly assumed that the modulus of elasticity of the workpiece at rolling temperatures is too low to significantly influence tension profiles.
In hot rolling, moreover, prior attempts to employ other than minimal interstand tensions, insufficient to have any noticeable effect on strip flatness, have met with inconsistent and sometimes highly unsatisfactory results. Because the factors governing interstand plastic deformation have been insufficiently understood, the results of these prior attempts have varied so that in some instances no appreciable effect was observed, while at other times severe reductions in width, or necking resulted. In extreme cases, interstand plastic deformation has been so drastic as to result in breaking of the strip.